The Frenchman, whose current deal runs out in the summer, will wrap up the new agreement before heading to the World Cup as a pundit for French television.
Wenger said: "Yes (it will be done), because I go to Brazil on the 10th of June."
A proud Wenger watched his Arsenal side win the FA Cup 3-2 in extra-time against Hull City at Wembley to end a trophy drought of nine years since they last annexed the Football Association's domestic cup competition.
The Gunners became the first team to overturn a two-goal deficit and lift the FA Cup since Everton beat Sheffield Wednesday in 1966.
Wenger said: "We live in a world where people tell you always what you have not (done), they never tell you that you have done something as well.
"I believe as well the quality of a club is the consistency and then the special players make you win the trophies.
"The quality of the consistency is important for the club and on that front we have been better than everybody else - there are only two clubs in Europe who have 17 years consecutively qualified for the Champions League and that consistency demands special values inside the club."
Arsenal, though, still have to resolve whether full-back Bacary Sagna will remain, the France defender's deal is also set to expire this summer with Manchester City a possible destination, before they can look to bring in new recruits.
"First, we have to wait for Sagna - what will he do? - and (goalkeeper Lukasz) Fabianski. After, we have to bring in two or three players to strengthen the squad that is for sure," said Wenger.
England World Cup hopeful Alex Oxlade-Chamberlain did not feature in the cup final squad as he continued to recover from a groin problem.
"Alex was desperate to play in the final, and pain-wise, he could have played," said Wenger. "But I judged him short physically and I felt that in the game, I wanted to play the players who were completely fit and prepared.
"He is a bit short physically. They said to me he can play 20 or 30, but you cannot program it like that, and so that is why I left him out.
"He is on the way up, but he needs more fitness work now. He is okay for England."